Asymptotics for Stieltjes polynomials, Padé-type approximants, and Gauss-Kronrod quadrature.

  1. Bello Hernández, M. 1
  2. De La Calle Ysern, B. 1
  3. Guadalupe Hernández, J.J. 1
  4. Lopez Lagomasino, G. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revue:
Journal d'Analyse Mathematique

ISSN: 0021-7670

Année de publication: 2002

Volumen: 86

Pages: 1-23

Type: Article

DOI: 10.1007/BF02786642 SCOPUS: 2-s2.0-0036354252 WoS: WOS:000175722100001 GOOGLE SCHOLAR

D'autres publications dans: Journal d'Analyse Mathematique

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Résumé

We study the asymptotic properties of Stieltjes polynomials outside the support of the measure as well as the asymptotic behaviour of their zeros. These properties are used to estimate the rate of convergence of sequences of rational functions, whose poles are partially fixed, which approximate Markov-type functions. An estimate for the speed of convergence of the Gauss-Kronrod quadrature formula in the case of analytic functions is also given.